If the sum of n terms of an A.P. is given by \(S_n = 3n + 2n^2\), then the common difference of the A.P. is
3
2
6
4
The third term of a G.P. is 4. The product of its first 5 terms is
\(4^3\)
\(4^4\)
\(4^5\)
None of these
If 9 times the 9th term of an A.P. is equal to 13 times the 13th term, then the 22nd term of the A.P. is
0
22
220
198
If \(x,\;2y,\;3z\) are in A.P., where the distinct numbers \(x,\;y,\;z\) are in G.P., then the common ratio of the G.P. is
3
\(\tfrac{1}{3}\)
2
\(\tfrac{1}{2}\)
If in an A.P., \(S_n = qn^2\) and \(S_m = qm^2\), where \(S_r\) denotes the sum of \(r\) terms of the A.P., then \(S_q\) equals
\(\dfrac{q^3}{2}\)
mnq
\(q^3\)
\((m+n)q^2\)
Let \(S_n\) denote the sum of the first \(n\) terms of an A.P. If \(S_{2n} = 3S_n\) then \(S_{3n} : S_n\) is equal to
4
6
8
10
The minimum value of \(4^x + 4^{1-x},\; x \in \mathbb{R}\), is
2
4
1
0
Let \(S_n\) denote the sum of the cubes of the first \(n\) natural numbers and \(s_n\) denote the sum of the first \(n\) natural numbers. Then \(\sum_{r=1}^n \dfrac{S_r}{s_r}\) equals
\(\dfrac{n(n+1)(n+2)}{6}\)
\(\dfrac{n(n+1)}{2}\)
\(\dfrac{n^2+3n+2}{2}\)
None of these
If \(t_n\) denotes the \(n\)th term of the series \(2 + 3 + 6 + 11 + 18 + \ldots\) then \(t_{50}\) is
\(49^2 - 1\)
\(49^2\)
\(50^2 + 1\)
\(49^2 + 2\)
The lengths of three unequal edges of a rectangular solid block are in G.P. The volume of the block is \(216\,\text{cm}^3\) and the total surface area is \(252\,\text{cm}^2\). The length of the longest edge is
12 cm
6 cm
18 cm
3 cm